"In the last election, Gallup's registered voter model — not its likely voter model — was a much more accurate predictor, with their likely model missing the mark in 2010 by 9 points right before the election," Benenson says. "That explains why Gallup's results are way out of line with a dozen recent swing state polls that show the president with a double-digit lead among women."

Romney's standing among female voters is "likely to cause major consternation among Obama supporters," Richard Eichenberg, a Tufts University political scientist, told USA Today. "If Mr. Romney has tied President Obama among women in swing states, then he has likely taken a step toward winning the election.

"But a word of caution is necessary," Eichenberg adds. "Although swing states share many similarities, President Obama's support among women is holding up well in some of them and less well in others. For example, his support among women is largely unchanged since the first debate in Ohio and Wisconsin, but it is definitely down in Colorado, Virginia and Florida."

Other national surveys have shown Obama having a large lead among women voters. In Gallup's national survey, the president remains ahead of Romney, 52 to 44 percent.